A parallel plate capacitor has area of each plate `A`, the separation between the plates is `d`. It is charged to a potential `V` and then disconnected from the battery. The amount of work done in the filling the capacitor Completely with a dielectric constant `k` is.

Options

A. `(1)/(2) (epsi_(0)AV^(2))/(d) [1-(1)/(k^(2))]`
B. `(1)/(2) (V^(2) epsi_(0)A)/(kd)`
C. `(1)/(2) (V^(2) epsi_(0)A)/(k^(2)d)`
D. `(1)/(2) (epsi_(0)AV^(2))/(d) [1-(1)/(K)]`

Answer

D

Explanation

Work done = decrease in energy ie `w = E_(1) -E_(2) = (1)/(2) (epsi_(0)A)/(d) v^(2) - (epsi_(0)Av^(2))/(2d) [1-(1)/(k)]`